{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 2, demo 4\n",
    "\n",
    "Bayesian Data Analysis, 3rd ed\n",
    "\n",
    "\n",
    "Probability of a girl birth given placenta previa (BDA3 p. 37).\n",
    "Calculate the posterior distribution on a discrete grid of points by multiplying the likelihood and a non-conjugate prior at each point, and normalizing over the points. Simulate samples from the resulting non-standard posterior distribution using inverse cdf using the discrete grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import preliz as pz\n",
    "\n",
    "pz.style.use(\"preliz-doc\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating posterior with non-conjugate prior in grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data\n",
    "a = 437\n",
    "b = 543\n",
    "\n",
    "# grid of nx points\n",
    "nx = 1000\n",
    "x = np.linspace(0, 1, nx)\n",
    "\n",
    "# compute density of non-conjugate prior in grid\n",
    "# this non-conjugate prior is same as in Figure 2.4 in the book\n",
    "pp = np.ones(nx)\n",
    "ascent = (0.385 <= x) & (x <= 0.485)\n",
    "descent = (0.485 <= x) & (x <= 0.585)\n",
    "pm = 11\n",
    "pp[ascent] = np.linspace(1, pm, ascent.sum())\n",
    "pp[descent] = np.linspace(pm, 1, descent.sum())\n",
    "# normalize the prior\n",
    "pp /= np.sum(pp)\n",
    "\n",
    "# unnormalized non-conjugate posterior in grid\n",
    "po = pz.Beta(a, b).pdf(x) * pp\n",
    "po /= np.sum(po)\n",
    "# cumulative\n",
    "pc = np.cumsum(po)\n",
    "\n",
    "# inverse-cdf sampling\n",
    "# get n uniform random numbers from [0,1]\n",
    "n = 10_000\n",
    "r = np.random.rand(n)\n",
    "# Map each uniform random number r to its corresponding x value\n",
    "# by finding the first index where r <= pc (inverse-CDF sampling)\n",
    "rr = x[np.searchsorted(pc, r)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot 3 subplots\n",
    "_, axes = plt.subplots(3, 1, sharex=True, figsize=(12, 8))\n",
    "\n",
    "for pdf, title, ax in zip((pz.Beta(a+1, b+1).pdf(x),pp, po),\n",
    "                        ('Posterior with uniform prior', 'Non-conjugate prior', 'Posterior with non-conjugate prior'),\n",
    "                        axes.ravel()):\n",
    "    ax.plot(x, pdf)\n",
    "    ax.set_title(title)\n",
    "    ax.set_yticks([])\n",
    "\n",
    "# set custom x-limits\n",
    "axes[0].set_xlim((0.35, 0.65));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, axes = plt.subplots(3, 1, sharex=True, figsize=(12, 8))\n",
    "\n",
    "for idx, (dens, title, ax) in enumerate(zip((po, pc, rr),\n",
    "                                            ('Non-conjugate posterior', 'Posterior cdf', 'histogram of posterior samples'),\n",
    "                                            axes.ravel())\n",
    "):\n",
    "    if idx == 2:\n",
    "        ax.hist(dens, bins=30, density=True)\n",
    "    else:\n",
    "        ax.plot(x, dens)\n",
    "        ax.set_title(title)\n",
    "    ax.set_yticks([])\n",
    "\n",
    "# set custom x-limits\n",
    "axes[0].set_xlim((0.38, 0.52));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Authors:\n",
    "- Aki Vehtari <aki.vehtari@aalto.fi>\n",
    "- Tuomas Sivula <tuomas.sivula@aalto.fi>\n",
    "- Osvaldo A. Martin <osvaldo.martin@aalto.fi>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "bda_py_demos",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
